Coding Method for Correction and Detection of Skewed Transitions in Parallel Asynchronous Communication Systems

1. A method of encoding to produce sets of codewords from sequences of digital electrical signals for asynchronous transmission over parallel communication channels without requiring acknowledgement of completion of each transmitted codeword, comprising the steps of: from four selectable non-negative integers t.sub.1, t.sub.2, s.sub.1, s.sub.2, selecting t.sub.1 as a maximum correctable number and t.sub.1 +s.sub.1 as a maximum detectable number of transitions that can be missing from a first transmitted codeword when a transition from a second transmitted codeword arrives, and selecting t.sub.2 as a maximum correctable number and t.sub.2 +s.sub.2 as a maximum detectable number of transitions which can arrive from the second transmitted codeword before all of the transitions of the first transmitted codeword arrive; using an encoder and a standard error correcting code (ECC), constructing ECC codewords of a word length sufficient to accommodate all information bits to be transmitted and having a minimum distance between any pair of ECC codewords of t.sub.1 +t.sub.2 +S+max{T,s}+1, where S=max{s.sub.1,s.sub.2 } and T=max{t.sub.1,t.sub.2 } and s=min{s.sub.1,s.sub.2 }; and using said encoder, unordering the ECC codewords by concatenating additional redundancy bits of a number sufficient that no resulting ECC codeword can be contained in another codeword in the code, said ECC codewords being capable of correcting up to t.sub.1 or t.sub.2, and detecting up to t.sub.1 +s.sub.1 or t.sub.2 +s.sub.2, skewed transitions that result from mixing of transitions from codewords transmitted in sequence.

2. The method of claim 1, wherein the unordering step includes the steps of: determining the weight of each of the ECC codewords; expressing that weight in a binary representation; and complementing the binary representation to produce said additional redundancy bits.

3. The method of claim 1, wherein the step of unordering includes the steps of: using a combinational logic circuit, determining the weight of each of the ECC codewords; using a divider circuit, dividing said weight by the quantity (t.sub.1 +t.sub.2 +S+max{T,s}+1) and generating the integer part thereof in binary representation; and using inverter circuitry, complementing the binary representation to produce said additional redundancy bits.

4. The method of claim 1, wherein the values of s.sub.1 and s.sub.2 are zero and the ECC codewords merely correct up to t.sub.1 and t.sub.2 skewed transitions.

5. The method of claim 1, wherein the sets of transmitted codewords have a length and are constructed by the steps of: using N(X,Y) to denote the number of coordinates in which X is 1 and Y is 0 and using N(Y,X) to denote the number of coordinates in which Y is 1 and X is 0; and encoding the sequences of digital signals into a set of transmitted codewords in which one of the following criteria is met for all pairs of transmitted codewords X and Y in each said set: (a) if (t.sub.1 -t.sub.2)(s.sub.1 -s.sub.2).gtoreq.0 and N(X,Y).ltoreq.N(Y,X), then at least one of the following three conditions occurs: 1. N(X,Y).gtoreq..tau.+1; 2. N(X,Y).gtoreq.T+1 and N(Y,X).gtoreq..rho.+1; or 3. N(X,Y).gtoreq.1 and N(Y,X).gtoreq.t.sub.1 +t.sub.2 +S+1; whereas if(t.sub.1 -t.sub.2)(s.sub.1 -s.sub.2)<0 and N(X,Y).ltoreq.N(Y,X), then at least one of the following four conditions occurs: 1. N(X,Y).gtoreq..tau.+1; 2. N(X,Y).gtoreq.T+1 and N(Y,X).gtoreq..rho.+1; 3. N(X,Y).gtoreq.t+1 and N(Y,X).gtoreq.t.sub.1 +t.sub.2 +s+1; or 4. N(X,Y).gtoreq.1 and N(Y,X).gtoreq.t.sub.1 +t.sub.2 +S+1; where t=min{t.sub.1,t.sub.2 }, .tau.=min{t.sub.1 +s.sub.1,t.sub.2 +s.sub.2 }, and .rho.=max{t.sub.1 +s.sub.1,t.sub.2 +s.sub.2 }.

6. A (t.sub.1,t.sub.2)-skew-tolerant (t.sub.1 +s.sub.1,t.sub.2 +s.sub.2)-skew,detecting code constructed by the method of claim 5.

7. The method of claim 5, including initiating a desired control protocol when the number of skewed transitions exceeds t.sub.1 or t.sub.2 provided the number of skewed transitions does not exceed t.sub.1 +s.sub.1 and t.sub.2 +s.sub.2.

8. A method of correcting and detecting skewed transitions in codewords transmitted asynchronously as sequences of digital electrical signals over parallel information communication channels without acknowledgement of completion of each transmission, comprising the steps of: from four selectable nonnegative integers t.sub.1, t.sub.2, s.sub.1, s.sub.2, selecting t.sub.1 as a maximum correctable number, and t.sub.1 +s.sub.1 as a maximum detectable number, of transitions that can be missing from a first transmitted codeword when a transition from a second transmitted codeword arrives, and selecting t.sub.2 as a maximum correctable number, and t.sub.2 +s.sub.2 as a maximum detectable number, of transitions which can arrive from the second transmitted codeword before all of the transitions of the first transmitted codeword arrive; using N(X,Y) to denote the number of coordinates in which X is 1 and Y is 0, and N(Y,X) to denote the number of coordinates in which Y is 1 and X is 0; using an encoder, creating a (t.sub.1,t.sub.2)-skew-correcting (t.sub.1 +s.sub.1,t.sub.2 +s.sub.2)-skew-detecting code by encoding codewords constituting sets in which one of the following criteria is met for all pairs of codewords X and Y in the set, assuming N(X,Y).ltoreq.N(Y,X): (a) if (t.sub.1 -t.sub.2)(s.sub.1 -s.sub.2).gtoreq.0, then at least one of the following three conditions occurs: 1. N(X,Y).gtoreq..tau.+1; 2. N(X,Y).gtoreq.T+1 and N(Y,X).gtoreq..rho.+1; or 3. N(X,Y).gtoreq.1 and N(Y,X).gtoreq.t.sub.1 +t.sub.2 +S+1; and (b) if (t.sub.1 -t.sub.2)(s.sub.1 -s.sub.2)<0, then at least one of the following four conditions occurs: 1. N(X,Y).gtoreq..tau.+1; 2. N(X,Y).gtoreq.T+1 and N(Y,X).gtoreq..tau.+1; 3. N(X,Y).gtoreq.t+1 and N(Y,X).gtoreq.t.sub.1 +t.sub.2 +s+1; or 4. N(X,Y).gtoreq.1 and N(Y,X).gtoreq.t.sub.1 +t.sub.2 +S+1; where t=min{t.sub.1,t.sub.2 }, T=max{t.sub.1,t.sub.2 }, s=min{s.sub.1,s.sub.2 }, S=max{s.sub.1,s.sub.2 }, .tau.=min{t.sub.1 +s.sub.1,t.sub.2 +s.sub.2 }, .rho.=max{t.sub.1 +s.sub.1,t.sub.2 +s.sub.2 }; and correcting, with a processor, skewed transitions as long as the values of t.sub.1 and t.sub.2 are not exceeded; and detecting with said processor skewed transitions when the value of either t.sub.1 or t.sub.2 is exceeded but the values of t.sub.1 +s.sub.1 and t.sub.2 +s.sub.2 are not exceeded.

9. In an information communication system wherein digital electrical signals are transmitted asynchronously in sequences and no acknowledgement of sequence completion is required, a method of decoding vectors containing error-free information represented by said signals and capable of detecting and correcting skewed transitions which mix the information from codewords transmitted in sequence, comprising the steps of: (a) with an asynchronous receiver, receiving one vector having information bits and redundancy bits resulting from a transition received on any of n parallel channels; (b) using a set processor, generating a first set of vectors from subsets of said one vector and removing from each vector in said first set all redundancy bits to provide an estimate of information bits; (c) using an encoder, encoding and unordering all bits remaining after the redundancy bits have been removed from each vector of said first set to create a second set of vectors corresponding to the vectors of said first set; (d) using a comparator, comparing each vector of said first set with a corresponding vector of said second set; and (e) using a gate circuit conditioned when one of the vectors of the first set is the same as its corresponding vector in the second set for outputting information bits corresponding to said one vector in said first set.

10. The method of claim 9, including repeating steps (b)-(e) for each said one vector received in successive steps (a).

11. An apparatus employing parallel asynchronous communication for transmitting codewords over parallel channels from a transmitter to a receiver without acknowledgement of transmission completion, comprising: (i) an encoder for constructing a set of codewords such that, for t=min{t.sub.1,t.sub.2 }, T=max{t.sub.1,t.sub.2 }, s=min{s.sub.1,s.sub.2 }, S=max{s.sub.1,s.sub.2 }, .tau.=min{t.sub.1 +s.sub.1,t.sub.2 +s.sub.2 }, and .rho.=max{t.sub.1 +s.sub.1,t.sub.2 +s.sub.2 }, one of the following criteria is met for all pairs of codewords X and Y, assuming N(X,Y).ltoreq.N(Y,X) in the set, where N(X,Y) denotes the number of coordinates in which X is 1 and Y is 0, and N(Y,X) denotes the number of coordinates in which Y is 1 and X is 0: (a) if(t.sub.1 -t.sub.2)(s.sub.1 -s.sub.2).gtoreq.0, then at least one of the following three conditions occurs: 1. N(X,Y).gtoreq..tau.+1; 2. N(X,Y).gtoreq.T+1 and N(Y,X).gtoreq..rho.+1; or 3. N(X,Y).gtoreq.1 and N(Y,X).gtoreq.t.sub.1 +t.sub.2 +S+1; whereas (b) if(t.sub.1 -t.sub.2)(s.sub.1 -s.sub.2)<0, then at least one of the following four conditions occurs: 1. N(X,Y).gtoreq..tau.+1; 2. N(X,Y).gtoreq.T+1 and N(Y,X).gtoreq..rho.+1; 3. N(X,Y).gtoreq.t+1 and N(Y,X).gtoreq.t.sub.1 +t.sub.2 +s+1; or 4. N(X,Y).gtoreq.1 and N(Y,X).gtoreq.t.sub.1 +t.sub.2 +S+1; where t.sub.1, t.sub.2, s.sub.1, and s.sub.2 are selectable nonnegative integers, t.sub.1 is a preselected maximum correctable number and t.sub.1 +s.sub.1 is a preselected maximum detectable number of transitions that can be missing from a first transmitted codeword when a transition from a second transmitted codeword arrives, t.sub.2 is a preselected maximum correctable number and t.sub.2 +s.sub.2 is a preselected maximum detectable number of transitions that can arrive from the second transmitted codeword before all the transitions of the first transmitted codeword arrive; and (ii) a decoder for decoding said codewords upon reception and (a) correcting up to one preselected number of skewed transitions in codewords transmitted in sequence when both t.sub.1 and t.sub.2 are not exceeded, and (b) detecting up to another preselected number of skewed transitions when said one preselected number of skewed transitions has been exceeded but both t.sub.1 +s.sub.1 and t.sub.2 +s.sub.2 are not exceeded.

12. The apparatus of claim 11, including means operative if the number of skewed transitions exceeds the value of either t.sub.1 or t.sub.2 to initiate a desired control operation.

13. In a system for transmitting codewords in the form of sequences of digital electrical signals asynchronously over n parallel communication channels without requiring acknowledgement of completion of transmission of each sequence, decoding apparatus capable of detecting and correcting skewed transitions which mix signals from codewords transmitted in sequence, comprising: means for generating a first set of vectors from subsets of a vector having information bits and redundancy bits resulting from a transition received on any of said n parallel channels; means for removing from each vector in said first set all redundancy bits to provide an estimate of information bits; means for reencoding the bits remaining after the redundancy bits have been removed from each vector of said first set to create a second set of vectors corresponding to those of said first set; means for unordering said reencoded remaining bits; means for comparing each vector of said first set with a corresponding vector of said second set; and means for outputting information bits corresponding to one of the vectors in said first set if and when it is the same as its corresponding vector in the second set.